Abstract

Singular limits of a class of evolutionary systems of partial differential
equations having two small parameters and hence three time scales are considered.
Under appropriate conditions solutions are shown to exist and remain uniformly
bounded for a fixed time as the two parameters tend to zero at different rates. A
simple example shows the necessity of those conditions in order for uniform bounds
to hold. Under further conditions the solutions of the original system tend to solutions
of a limit equation as the parameters tend to zero.

This is a post-peer-review, pre-copyedit version of an article published in Archive for Rational Mechanics and Analysis. The final authenticated version is available online at: https://link.springer.com/journal/205